This is a grossly overpowered suggestion, but I'm going to throw it out there anyway:
Why not have a console that gives this bonus:
+1 to bridge officer allowed rank.
One console for each field. You could have a science ship that allowed for a Lt. commander tactical or engineering officer. Or a fleet/advanced escort with a higher level science or engineering officer. Or with both a commander and Lt. commander level tactical officers.
The tradeoff is you lose a console slot which could have been utilized for something else, like an EPS or RCS console or weapon buff console. Also, you still would not be able to train the rare skills outside your profession, so for example; you'd have to get lucky with a rare boff reward if you wanted emergency power to shields III on a science ship or escort.
Overpowered? Possibly. Imbalanced? Not if it benefits all ship classes and has a decent drawback.